John W. Galbraith

TESTING FOR ASYMMETRY IN THE LINK BETWEEN THE YIELD SPREAD AND OUTPUT IN THE G-7 COUNTRIES

The difference in yields between long-term and short-term securities has been used both as a business cycle leading indicator and as an indicator of the current impact of monetary policy. This paper tests for an asymmetry, in the form of a threshold effect, such that the impact of the yield spread on output is greater on one side of the threshold than the other. The test allows for an unknown threshold, and the asymptotic distribution of the resulting statistic is obtained by the method of Hansen (1996). We test using data from each of the G-7 countries, and find that, while the yield spread does generally show a signifcant link with output, only in the U.S. and Canada is there strong evidence of an asymmetry of this type. The evidence of asymmetry that we find suggests a high value of the threshold in both the U.S. and Canada.

Taxation, smuggling and demand for cigarettes in Canada: evidence from time-series data.

This study analyzes Canadian cigarette consumption and taxation between 1980 and 1994, a period in which there have been large price rises and declines, and a dramatic increase in the consumption of contraband tobacco products. We examine elasticities of legal cigarette sales and total sales (including contraband) with respect to the price of legal cigarettes and various other factors. The growth of the contraband market since 1987 appears to have created two classes of cigarette--taxed and untaxed--with responses to changes in the legal price that are respectively higher, and lower, than was previously the case. The sensitivity of total cigarette sales to the taxation instrument is much lower than it would appear from sales of taxed cigarettes alone.

Content horizons for univariate time-series forecasts

Abstract This paper investigates the maximum horizon at which conditioning information can be shown to have value for univariate time series forecasts. In particular, we consider the problem of determining the horizon beyond which forecasts from univariate time series models of stationary processes add nothing to the forecast implicit in the unconditional mean. We refer to this as the content horizon for forecasts, and provide a formal definition of the corresponding forecast content function at horizons s =1,… S . This function depends upon parameter estimation uncertainty as well as on autocorrelation structure of the process. We show that for autoregressive processes it is possible to give an asymptotic expression for the forecast content function, and show by simulation that the expression gives a good approximation even at modest sample sizes. The results are applied to the growth rate of GDP and to inflation, using US and Canadian data.

Estimating Intertemporal Quadratic Adjustment Cost Models with Integrated Series

The authors consider the estimation of parameters in Euler equations where regressand and regressors may be nonstationary, and propose a several-stage procedure requiring only knowledge of the Euler equation and the order of integration of the data. This procedure uses the information gained from pretesting for the order of integration of data series to improve specification and estimation. The authors can also offer an explanation of the frequent empirical finding that discount rates and adjustment costs are poorly estimated. Both analytical and experimental (Monte Carlo) results are provided. Copyright 1991 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Inference about trends in global temperature data

Interpretation of the effects of increasing atmospheric carbon dioxide on temperature is made more difficult by the fact that it is unclear whether sufficient global warming has taken place to allow a statistically significant finding of any upward trend in the temperature series. We add to the few existing statistical results by reporting tests for both deterministic and stochastic non-stationarity (trends) in time series of global average temperature. We conclude that the statistical evidence is sufficient to reject the hypothesis of a stochastic trend; however, there is evidence of a trend which could be approximated by a deterministic linear model.

Credit Rationing and Threshold Effects in the Relation between Money and Output

The possibility that the effect of monetary policy on output may depend on whether credit conditions are tight or loose can be expressed as a non-linearity in the relation between real money supply and output, of which a simple case is a threshold effect. In this case, consistent with the credit-rationing model of Blinder (1987), the monetary variable has a more powerful effect if it is below some threshold than when it is above. Testing for the importance of this threshold is straightforward if the appropriate threshold value is known a priori, but where the value is not known and must be chosen based on the sample, the testing problem becomes more difficult. We apply recently-developed tests applicable in this situation to both US and Canadian data, and find substantial evidence of a threshold effect, particularly in US data. However, the estimated threshold values are high. Copyright 1996 by John Wiley & Sons, Ltd.

ESTIMATION OF THE VECTOR MOVING AVERAGE MODEL BY VECTOR AUTOREGRESSION

ABSTRACT We examine a simple estimator for the multivariate moving average model based on vector autoregressive approximation. In finite samples the estimator has a bias which is low where roots of the characteristic equation are well away from the unit circle, and more substantial where one or more roots have modulus near unity. We show that the representation estimated by this multivariate technique is consistent and asymptotically invertible. This estimator has significant computational advantages over Maximum Likelihood, and more importantly may be more robust than ML to mis-specification of the vector moving average model. The estimation method is applied to a VMA model of wholesale and retail inventories, using Canadian data on inventory investment, and allows us to examine the propagation of shocks between the two classes of inventory.

Estimation of a linear regression model with stationary ARMA(p, q) errors

Abstract It is well known that consistent estimation of a linear regression model with a stationary Gaussian ARMA process in the errors can be carried out by maximum likelihood or, alternatively, by two-stage procedures involving estimation of the nuisance parameters followed by feasible generalized least squares for the model parameters. We show that the estimators coincide up to O p (T − 3 2 ) and derive the variance to O(T−2), which up to terms of this order is the same for both estimators. Considering the form of the error covariance matrix for an ARMA(p,q) process allows us to examine a computationally convenient algorithm for estimation of the parameters of the regression model. Finally we provide a Monte Carlo comparison of the small-sample properties of OLS and two versions of the proposed estimator.

Nonparametric Tests of the Unbiasedness of Olympic Figure-Skating Judgments

We use recently developed nonparametric tests for orthogonality to test the null hypothesis of an absence of national bias in the judging of Olympic figure-skating events. The results, and accompanying parametric estimates, offer strong evidence of a small bias which changes little across time. There is also some evidence that the bias is more marked for skaters who are medal contenders than for less strong competitors.

The GLS Transformation Matrix and a Semi-recursive Estimator for the Linear Regression Model with ARMA Errors

For a general stationary ARMA( p,q ) process u we derive the exact form of the orthogonalizing matrix R such that R ′ R = Σ −1 , where Σ = E ( uu ′) is the covariance matrix of u , generalizing the known formulae for AR ( p ) processes. In a linear regression model with an ARMA( p,q ) error process, transforming the data by R yields a regression model with white-noise errors. We also consider an application to semi-recursive (being recursive for the model parameters, but not for the parameters of the error process) estimation.